A histogram is a type of chart that allows us to visualize the distribution of values in a dataset.
We say that a histogram is left skewed if it has a “tail” on the left side of the distribution:
Note: Sometimes a left skewed histogram is also referred to as a negatively skewed histogram.
A left skewed histogram has the following two properties:
1. The peak of the distribution is on the right side.
2. The mean is less than the median.
What Causes a Histogram to Be Left Skewed?
A histogram is left skewed when it is uncommon for a variable to take on a small value and much more common for a variable to take on values concentrated around a larger value.
One real-life example of a left skewed histogram would be exam scores among students.
Most students might score between 70 and 90 on a particular exam and it’s extremely uncommon for many students to score near a zero.
When we create a histogram to visualize the distribution of exam scores for some class, it will naturally be left skewed:
Why is the Mean Less than the Median in a Left Skewed Histogram?
In a left skewed histogram, the mean is less than the median because the high frequency of values on the right side of the distribution causes the median value to be larger.
As a simple example, suppose we have the following dataset that contains the exam scores of 20 students in a class:
Dataset: 24, 45, 56, 71, 78, 80, 81, 81, 82, 83, 84, 85, 85, 89, 91, 91, 92, 93, 96, 97
Here are the mean and median values of this dataset:
- Mean: 79.2
- Median: 83.5
The mean value is dragged lower by the students who scored very low while the median value is located at the “middle” value of scores, which is 83.5.
If we plot this distribution, it would be a left skewed histogram with most of the values concentrated on the right side of the histogram.
The Difference Between Right Skewed & Left Skewed Histograms
The opposite of a left skewed histogram is a right skewed histogram.
This is a type of histogram that has a “tail” on the right side of the distribution:
This type of histogram has the following properties:
1. The peak of the distribution is on the left side.
2. The mean is greater than the median.
Notice that these are the exact opposite properties of a left skewed histogram.
Read more about right skewed histograms in this tutorial.
The following tutorials provide additional information about histograms:
How to Estimate the Mean and Median of Any Histogram
How to Estimate the Standard Deviation of Any Histogram
How to Describe the Shape of Histograms